Multiply the following complex numbers: $({5-2i}) \cdot ({-5+2i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5-2i}) \cdot ({-5+2i}) = $ $ ({5} \cdot {-5}) + ({5} \cdot {2}i) + ({-2}i \cdot {-5}) + ({-2}i \cdot {2}i) $ Then simplify the terms: $ (-25) + (10i) + (10i) + (-4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -25 + (10 + 10)i - 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -25 + (10 + 10)i - (-4) $ The result is simplified: $ (-25 + 4) + (20i) = -21+20i $